Traditionally, the neurophysiological mechanisms of cognitive processing have been investigated at the single cell level. Here we show that the dynamic, millisecond-by-millisecond, interactions between neuronal events measured by local field potentials are modulated in an orderly fashion by key task variables of a space categorization task performed by monkeys. These interactions were stronger during periods of higher cognitive load and varied in sign (positive, negative). They were observed both within area 7a of the posterior parietal cortex and between symmetric 7a areas of the two hemispheres. Time lags for maximum interactions were longer for opposite- vs. same-hemisphere recordings, and lags for negative interactions were longer than for positive interactions in both recording sites. These findings underscore the involvement of dynamic neuronal interactions in cognitive processing within and across hemispheres. They also provide accurate estimates of lags in callosal interactions, very comparable to similar estimates of callosal conduction delays derived from neuroanatomical measurements (Caminiti et al., 2013).